Domanda del libro di testo
In Exercises 49–52, a single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 2 the second time.
673
views
Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 9, Problema 49
Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1/2+2/3+3/4+⋯+ 14/(14+1)
Guida verificata passo dopo passo1
Identify the pattern in the sum: each term has the form \( \frac{i}{i+1} \), where \( i \) starts at 1 and increases by 1 for each term.
Determine the number of terms in the sum. Since the last term is \( \frac{14}{14+1} \), the index \( i \) goes from 1 to 14.
Write the summation notation using the index \( i \), the lower limit 1, and the upper limit 14, with the general term \( \frac{i}{i+1} \).
Express the sum as: \[ \sum_{i=1}^{14} \frac{i}{i+1} \]
This notation compactly represents the entire sum \( \frac{1}{2} + \frac{2}{3} + \frac{3}{4} + \cdots + \frac{14}{15} \).
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Summation Notation
Summation notation is a concise way to represent the sum of a sequence of terms using the sigma symbol (∑). It includes an index of summation, lower and upper limits, and a general term formula. This notation simplifies writing long sums and helps in analyzing series.
Video consigliato:
05:18
Interval Notation
Index of Summation and Limits
The index of summation (commonly i) represents the variable that changes in each term of the sum. The lower limit indicates where the summation starts, and the upper limit shows where it ends. Correctly identifying these limits is essential to accurately express the sum.
Video consigliato:
03:50Adding & Subtracting Like Radicals
General Term of the Sequence
The general term defines the formula for each term in the sum based on the index i. For the given sum, each term is a fraction with numerator i and denominator i+1. Recognizing this pattern allows writing the sum compactly using summation notation.
Video consigliato:
4:45Geometric Sequences - General Formula
Pratica correlata
Domanda del libro di testo
Use the formula for nCr to solve Exercises 49–56. An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?
758
views
Domanda del libro di testo
Use the Binomial Theorem to expand each expression and write the result in simplified form. (x3 +x-2)4
689
views
Domanda del libro di testo
Express each repeating decimal as a fraction in lowest terms.
924
views
Domanda del libro di testo
Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
906
views
Domanda del libro di testo
Express each repeating decimal as a fraction in lowest terms. 0.6 (repeating 6)
1055
views